Chapter 7 of Class 12 Maths, titled Integrals, is one of the most important and lengthiest chapters in the NCERT textbook. This chapter introduces the concept of integration, which is basically the reverse process of differentiation. Students will learn about indefinite and definite integrals, properties of integrals, and methods of integration such as substitution, partial fractions, and by parts. This chapter is the foundation for understanding advanced calculus and is often seen in both board exams and entrance exams like JEE.
I’m writing this article because many students find the topic of integration confusing when they see too many formulas and methods all at once. When I was preparing for boards, I struggled with deciding which method to use for a given question. With time and practice, I realised that understanding the logic behind each method is the key. This chapter is very scoring once you get the hang of it, and having access to the official NCERT PDF makes revision more convenient. The chapter not only carries heavy weightage in the CBSE board exams but also appears frequently in competitive exams, making it very important to study in depth.
What You Will Learn in Chapter 7: Integrals
Chapter 7 covers a wide range of topics, and here is a quick breakdown of the major concepts:
1. Indefinite Integrals
- Introduction to antiderivatives
- Basic integration formulas
- Integration using substitution method
- Integration using partial fractions
- Integration by parts
2. Definite Integrals
- Definite integral as the limit of a sum
- Fundamental Theorem of Calculus
- Evaluation of definite integrals using substitution
- Properties of definite integrals
3. Application-Based Problems
- Questions involving combination of methods
- Questions where you have to simplify expressions before integrating
- Some MCQ-style and reasoning-based questions also appear in exams
It’s important to practise questions from each method because that’s how you’ll know which formula applies in which situation.
Why Chapter 7 Is So Important
Integrals are not just a chapter in the textbook, but a concept used across maths, physics, and engineering. Many real-life problems like calculating area under curves, total distance covered, and average value of functions depend on integrals. CBSE often asks at least one 6-mark question from this chapter, and JEE Main or Advanced usually includes 1-2 questions related to definite integrals or integration techniques.
From personal experience, this chapter looks long, but if you divide it into small sections and practise regularly, it becomes manageable. Understanding when to apply substitution or partial fractions comes with solving a variety of examples. NCERT exercises are well-designed to cover most of the standard question types. I strongly suggest solving all solved examples before attempting the exercises.
